Path optimization (also known as trend filtering) aims at finding an optimal path based on a raw path, which minimizes a cost as a function of both the raw path and the optimal path to be computed. Path optimization has wide application, including robotics, aviation, and finance. For example, path optimization may be used to smooth a shaking raw camera path for video stabilization.
Linear programming (LP) is a mathematical technique for maximizing or minimizing a linear function of several variables, such as output or cost. Quadratic programming (QP) is a process of solving a special type of mathematical optimization problem—specifically, a (linear constrained) quadratic optimization problem, that is, the problem of optimizing (minimizing or maximizing) a quadratic function of several variables subject to linear constraints on these variables.